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Consider the graph given below. Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above. Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2 Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6 Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2 Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2

Sagot :

MrRoyalidn

The sequences of transformations that could be applied to the parent function are (e) Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units

How to determine the sequence of transformation?

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(3, 0) and (0, 6)

Calculate the equation of the line using

[tex]g(x) = \frac{y_2 - y_1}{x_2 -x_1} * (x - x_2) + y_2[/tex]

This gives

[tex]g(x) = \frac{6 - 0}{0 -3} * (x - 0) + 6[/tex]

Evaluate the quotient

g(x) = -2 * (x) + 6

Expand

g(x) = -2x + 6

This means that the equation of the line is:

g(x) = -2x + 6

So, we have:

f(x) = x as the parent function and g(x) = -2x + 6 as the transformed function.

The transformations from f(x) to g(x) are as follows:

  • Reflect over the y-axis i.e. f'(x) = -f(x) = -x
  • Stretch vertically by a factor of 2 i.e. f"(x) = 2f'(x) = -2x
  • Shift up by 6 units i.e. g(x) = f"(x) + 6 = -2x + 6

Hence, the sequences of transformations that could be applied to the parent function are (e) Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units

Read more about transformation at:

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View image MrRoyal